Question

Qual é a derivada total dz/dt, sendo z = x2 -8xy - y3 , onde x(t) = -t e y (t) = t ?

Answer 1

d/dt (z) = d/dt (x²) - d/dt (8xy) - d/dt (y³) = 2x dx/dt - 3y² dy/dt - (8x.dy/dt + y . 8dx/dt )


d/dt (z) = 2(-t).(-1) - 3t² . (1) - ( 8.(-t).1 + t. 8.(-1) ) = 2t - 3t² -( -8t -8t) = 2t+16t - 3t² = 18t - 3t²

Logo: d(z)/dt = 18t - 3t²